1. Field of the Invention
The invention relates to an apparatus adapted to determine the representative parameters of rheological properties of viscoelastic fluids, particularly dilute solutions of macromolecular compositions, the apparatus translating the variations of behaviour during flow in comparison to Newtonian fluids by means of the relationship between stress and strain rate.
2. Discussion of Prior Art
It is noted that, in fluid mechanics, a fluid in which the relation between the stress tensor and the strain rate tensor, or the behavioural law, is linear. It will be remembered that a stress, expressing the force applied to a portion of fluid surface, is to have the dimensions of pressure, while a strain rate, expressing a velocity gradient, is expressed as the inverse of time. Finally, the ratio of stress to strain rate is a dynamic viscosity. In an isotropic Newtonian fluid, the viscosity is a constant depending uniquely on the temperature and the pressure. More precisely, the stresses are proportional to the rate of shear.
A vast number of fluids do not obey this simple behavioural law relating stress and strain rate. It is thus necessary to complement the Newtonian term of the behavioural law by a supplemental term taking into account the presence of additional stresses. In the case of fluids having complex behavior, such as solutions of macromolecular compositions, the additional stresses are a function on one hand of the relative difference between the inverse of the maximum strain rate and the relaxation time of the macromolecular composition and on the other hand of a stress which expresses the intensity of forces transmitted to the fluid by the macromolecular composition in the course of its deformation. This type of behavior is known as viscoelastic. In general, for low strain rates, the behavior of these fluids is practically Newtonian.
This has been observed particularly for macromolecular composition solutions which are formed by polymerization of basic units into long chains.
Studies have been published in scientific literature, relating to the anomalies of non-turbulent flows, in the steady state as solutions of macromolecular compositions of elevated molecular weights having elastic chains, such as polyethylene oxides. It appears that generally these anomalies manifest themselves when fluid, at least in certain regions, is subjected to extensional deformation. Such flows have been achieved at the stagnation point of Pitot tube sensors, at the inlet and at the outlet of an orifice, and in a flow in front of and around an obstacle having a progressive curvature, such as a circular cylinder. It appears that the presence of a macromolecular composition introduces significant variations from the fields of flow and pressure of the types of flow mentioned. In the case of a Pitot tube, the stagnation pressure can be smaller than the dynamic pressure. In flows across orifices, the necessary driving pressure to establish a given flow can become greater than that which is required by a Newtonian fluid of equal flow rate. The drag of a circular cylinder of small diameter can clearly be greater than the drag in the solvent, etc. The Pitot tube and the orifices offer the advantage of permitting the taking of simple quantitative measurements which can be related to rheological parameters of the fluid. For measurements with a Pitot tube, one drives, for example, a probe over a circular trajectory at the end of a turning arm. For measurements of flow across an orifice, one measures the differential pressure between the fluid immediately upstream and downstream of the orifice for a given flow, readily obtained by pressurizing the liquid with a piston having a given velocity of displacement in a cylinder of known cross-section.
The compilation of published studies, and particularly those which utilize the Pitot tube technique and that of the flow in an orifice, show that for solutions of polyethylene oxide having an elevated molecular weight, pressure anomalies begin to appear at the critical values of the strain rate, and, furthermore, that the increase in abnormal pressure is proportional to the excess of the strain rate over the critical values. The critical values and the coefficients of proportionality are functions of the concentration of the macromolecular composition. These results imply that the behavior during flow of diluted solutions of macromolecular compositions of the type referred to above can be defined by two parameters, both of which are functions of the concentration; a relaxation time and a specific stress. The specific stress is proportional to the concentration for sufficiently high dilutions. This behavior conforms to that of a theoretical model which is based upon the hypothesis that elastic molecules do not extend to a significant extent except at strain rates greater than the critical value, and that they orient themselves along a preferred direction adjacent to that of the principal strain rate.
The devices utilized in published studies make it possible to determine couples of correlated values, the values of one couple being respectively representative of a strain rate and of a corresponding pressure. The results on a rectangular coordinate graph of value couples yield points from which a representative curve can be traced. This curve causes the appearance, beyond a particular value of strain rate called the critical strain rate, of abnormal behavior of solutions of macromolecular compositions. The determination of the critical strain rate suffers from imprecision, particularly when the solution is very dilute and when this behavior is close, by virtue of the low value of the specific stress, to Newtonian behavior. This is also true for concentrated solutions or slightly dilute solutions of certain polymers for which the transition between Newtonian and abnormal behavior is progressive.